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Q3.

Expert-verified

Algebra 1

Found in: Page 302

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Solve each inequality. Then graph it on a number line.
$p - 4 < - 7$

The required value of x is $(- \infty, - 3)$ . The graph on the number line is,

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\leq or \geq$ , use the bracket or a solid circle at that endpoint.

Properties of inequality:

$1. b \leq c \Rightarrow b \pm a \leq c \pm a 2. b \leq c \Rightarrow a b \leq a c, if a > 0 3. b \leq c \Rightarrow a b \geq a c, if a < 0$

Step 2. Solve the inequality for x.

In order to solve the inequality:

$p - 4 < - 7$

Add 4 both sides of the inequality, as

$p - 4 < - 7 p - 4 + 4 < - 7 + 4 p < - 3$

Thus, the solution of the given inequality is every number is strictly less than $- 3$ , this can be represented in the interval form, as width="69" style="max-width: none; vertical-align: -4px;" $(- \infty, - 3)$ .

Step 3. Plot the graph on the number line.

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point $- 3$ is strict, so use a hollow circle at point $- 3$ . And the solution interval at left endpoint $- \infty$ , thus every point strictly less than $- 3$ is in the solution interval of given inequality. The graph of the solution of inequality is shown below:

Most popular questions for Math Textbooks

Solve each inequality. Check your solution.

$18 \leq - 2 x + 8$

Solve $p + 8 \leq 18$

F role="math" localid="1647844731947" ${p | p \geq 10}$

G ${p | p \leq 10}$

H ${p | p \leq 26}$

J ${p | p \geq 126}$

Drew currently has 31 comic books in his collection. His friend Connor has 58 comic books. How many more comic books does Drew need to add to his collection in order to have a larger collection than Connor?

A no more than 21

B 27

C at least 28

D more than 30

Solve each inequality. Check your solution.

$- 2 (4 b + 1) < - 3 b + 8$

Define a variable, write an inequality, and solve the problem. Check your solution. The difference of a number and 4 is no more than 8.

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